Problem: $g(t) = t^{2}+5$ $f(t) = 5t^{3}-2t^{2}-5(g(t))$ $h(n) = -7n^{3}+2n^{2}+n+4(f(n))$ $ g(f(2)) = {?} $
Answer: First, let's solve for the value of the inner function, $f(2)$ . Then we'll know what to plug into the outer function. $f(2) = 5(2^{3})-2(2^{2})-5(g(2))$ To solve for the value of $f$ , we need to solve for the value of $g(2)$ $g(2) = 2^{2}+5$ $g(2) = 9$ That means $f(2) = 5(2^{3})-2(2^{2})+(-5)(9)$ $f(2) = -13$ Now we know that $f(2) = -13$ . Let's solve for $g(f(2))$ , which is $g(-13)$ $g(-13) = (-13)^{2}+5$ $g(-13) = 174$